David Osten awarded with internship at the German Bundestag from Heraeus Foundation

Quantum Field Theory

One-loop contribution to the anomalous magnetic dipole moment This is the mandatory Quantum Field Theory course of the Master in Theoretical Physics at the University of Wrocław. It is tailored towards master and PhD students who are familiar with

quantum mechanics
electrodynamics
special relativity
quantum electrodynamics.

There are many good books on the subject, four that I like are

[PeskSchr] Peskin, Schroeder: An introduction to quantum field theory
[Ryder] Ryder: Quantum Field Theory
Weinberg: The Quantum Theory of Fields, Volume 1 & 2
Zee: Quantum Field Theory in a Nutshell.

We will follow mostly the first one in the lectures. There will be 2 hours of lectures and 2 hours of tutorial each week. Exercises will be posted here a week before the tutorial they are discussed in. Please keep in mind that active participation in the tutorials is important to pass the course. Prof. Pok Man Lo will be in charge of the tutorials with M.Sc. Alex Swash as assistant. Please fell free to contact them or me if you have any questions. For information about credits points, please refer to the syllabus or contact me directly.

Important: Students will be assigned to exercise problems by the system described here at the Monday, 9:00 pm, before the tutorial. Please indicate your preferences by then.

Exam: After a majority vote, we decided together that the written exam for this course will take place on Thursday, the 27th of June 2024, at 13:00 in room 447 (the one where we also have our classes). It will take two hours and we will discuss a practice exam in the last tutorial to help you preparing for it. Please be there five minutes earlier such that we can start on time. Also note that you need to have more than 50% of the points from the exercises assigned to you to qualify for the exam. You can check your points here on the website, or, if you are in doubt, with me or Alex.

Retake Exam: As discussed via email, you have the chance to take part in the retake exam on Friday, the 6th of September 2024, at 10:00 . Exactly the same conditions as described for the exam above will apply. If you would like to take part in the retake exam, please send me a quick message via email such that I have an estimated head count and can bring the right number of exams.

Additional material for the individual lectures, including the exercises which we discuss in the tutorials, is given below:

Lectures

Reminder of spin 0 and 1/2 fields
Lecture23.02.2024 09:15, notes, show recording
Tutorial23.02.2024 07:15, exercise
Reading: [PeskSchr] sections one and two

Please note that there are no exercise assignments for the first seminar. Instead, we continue with the lecture.
Reminder of spin 1 fields and abelian gauge symmetries
Lecture01.03.2024 09:15, notes
Tutorial01.03.2024 07:15, exercise
Reading: [Ryder] sections 3.3 and 4.4
Non-abelian gauge symmetries and Lie groups
Lecture08.03.2024 09:15, notes
Tutorial08.03.2024 07:15, exercise
Reading: [PeskSchr] section 15 except for 15.3 or alternatively [Ryder] sections 3.5 and 3.6
Path integral in quantum mechanics and for the scalar field
Lecture15.03.2024 09:15, notes
Tutorial15.03.2024 07:15, exercise
Reading: [PeskSchr] section 9.1
Generating functional, interactions and Feynman rules
Lecture22.03.2024 09:15, notes, Feynman rules from path integral, show recording
Tutorial22.03.2024 07:15, exercise
Reading: [PeskSchr] section 9.2

From here on, we will often expand the path integral using a perturbation parameter, like a coupling strength. The resulting power series can be elegantly organized in terms of Feynman diagrams. Because of the importance, I would like to show you all the step of this computation which is to long for the lecture. Therefore, we will use the last 40 minutes of the tutorial to discuss how Feynman diagrams and symmetry factors explicitly arise from the path integral. Above you will also find a copy of the computation for your reference.
Path integral for fermions, Grassmann numbers, chiral anomaly (in the exercise)
Lecture05.04.2024 08:15, notes, show recording
Tutorial05.04.2024 07:15, exercise
Reading: [PeskSchr] section 9.5
Path integral for spin-1 bosons, ghost fields
Lecture12.04.2024 08:15, notes, show recording
Tutorial16.04.2024 06:15, exercise
Reading: [PeskSchr] section 9.4
One loop effects in QED: field-strength renormalisation and self-energy
Lecture16.04.2024 08:15, notes, show recording
Tutorial19.04.2024 06:15, exercise
Reading: [PeskSchr] section 7.1
Dimensional regularisation and superficial degree of divergence
Lecture19.04.2024 08:15, notes, show recording
Tutorial26.04.2024 06:15, exercise
Reading: Peskin&Schroeder sections 7.5 and 10.1
One-loop renoramlised $\phi^4$ theory
Lecture26.04.2024 08:15, notes, show recording
Tutorial17.05.2024 06:15, exercise
Reading: [PeskSchr] section 10.2
Renormalisation group flow
Lecture17.05.2024 08:15, notes, show recording
Tutorial24.05.2024 06:15, exercise
Reading: [PresSchr] section 12.1
The Callan-Symanzik equation and $\beta$ -functions
Lecture24.05.2024 08:15, notes
Tutorial29.05.2024 06:15, exercise
Reading: [PresSchr] sections 12.2
Gravity, quantum gravity, one-loop $\beta$ -functions of a two-dimensional $\sigma$ -model and string theory
Lecture29.05.2024 08:15, notes
Tutorial06.06.2024 12:15, exercise
Reading: David Tong's lecture notes on String Theory section 7.1, original article Phys.Rev.Lett. 45 (1980) 1057
Spontaneous symmetry breaking and the Higgs mechanism
Lecture06.06.2024 14:00, notes, practice exam, Alex's notes
Tutorial11.06.2024 12:15, exercise
Reading: [PresSchr] sections 11.1 and 20.1

There is no problem sheet for this lecture. In the tutorial, which takes place right before the last lecture, we discuss the practice exam. Moreover please note that Alex has be so kind to prepare extended notes on the renormalisation of the $\phi^4$ theory.
BRST symmetry, physical Hilbert space
Lecture14.06.2024 15:00, notes
Reading: [PeskSchr] section 16.2-16.4